How English is the English: Many modern English people have Celtic blood, in that many of their ancestors were actually surviving Britons rather than immigrant German. This is particularly evident in western England, especially Cornwall, which retained some Celtic language until post medieval times. But even in the east there is evidence that many Britains survived the Germanic takeover, wars, plagues and westward flight of many of their countrymen. Survival of British enclaves is detectable in surviving place-names like Walton, "settlement of the Britons".Some of the early Anglo-Saxon kingdoms may have had Celtic roots, they certainly had largely Celtic populations.Northumbria, one of the most powerful of German kingdoms, probably had a mostly native population. It has even been suggested that Cerdic, founder of the royal house of Wessex, may have been a Briton, with the name Coraticus. These Britons were gradually absorbed and "Germanized" by the Anglo-Saxons, rather more effectively and totally than their ancestors had been Romanized.

I have that book. I don't always agree with everything Simon James has to say, but the quote in the original post could be right.

The Anglo-Saxons didn't sweep across the island in a few years. It took them a couple of centuries, and they succeeded in part by allying rival British chieftains to themselves and by taking advantage of internecine British tribal conflicts. For a time, in the late 5th century, the Britons had the upper hand and actually drove the Anglo-Saxons back into their eastern enclaves and practically out of the island. One of their leaders, a man called "Riotimus" by Jordanes, actually led an army of Britons into Gaul and defeated the Saxons who had settled along the Loire before falling victim to Roman intrigue and a much larger force of Visigoths. ("Riotimus" may have been a title - like "High King" - and this particular Riotimus could have been the historical Arthur.)